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Review of wearout life

Lifetime of aluminum electrolytic capacitors isgenerally specified as the time under certain con-ditions of applied DC voltage, ripple current, andambient conditions (temperature, airflow,heatsinking) at which the capacitor’s electricalparameters have drifted out of some specified lim-its. The ESR is the first to go, and perhaps it hasdrifted so high that soon the capacitor will eitherrun so hot that it suddenly shorts out or that it rup-tures its safety vent and begins to dry out and driftopen circuit. This lifetime is also known as WearoutLife, Expected Life, Operating Life (Lop), or Use-ful Life. The wearout process is rarely driven byevaporation and escape of the electrolyte unlessthe safety vent is compromised due to high leak-age current and pressure buildup. True dryout hasan effect similar to wearout but usually occurs incapacitors smaller than 20 cm3 or in capacitors ofolder design with poor seal technology. Our published wearout lifetime model followsfrom the results of life tests. The effect of tem-perature may also be derived from the Arrheniusequation. This derivation and a comparison of volt-age derating equations are presented in our paper“Deriving Life Multipliers for Aluminum Electro-lytic Capacitors.” The life model is

L = Lb × Mv × 2((Tm-Tc)/10) (1)

Reliability of CDE Aluminum Electrolytic Capacitors

Sam G. Parler, Jr., P.E.Cornell Dubilier

140 Technology PlaceLiberty, SC 29657sparler@cde.com

Here, Lb is the base life at an elevated core tem-perature Tm. See Table 1 below. Mv is a voltagemultiplier, usually equal to unity at the full ratedDC voltage, and greater than one at lower DC volt-

Abstract— All design engineers who consider using aluminum electrolytic capacitorswant to know how long they will last and how many they can expect to fail. Manyengineers do not realize that these are actually two different but related questions.In this paper we define life and reliability in a manner that will hopefully make thedistinction clear, and we compare, contrast, and combine life and reliability models

in a way that will allow design engineers to predict from their application conditionsnot only how long before the capacitors begin to wear out, but also what the ex-

pected failure rate is during the useful life of the capacitors.

Table 1: CDE Lb and Tm values used in life andreliability models

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ages. Cornell Dubilier generally uses

Mv = 4.3 - 3.3Va/Vr (2)

where Va is the applied DC voltage and Vr is therated DC voltage. The rated DC voltage is definedsuch that the peak applied voltage should not ex-ceed this value. One complication arises because the electrolyteresistance Ro is a function of the actual core tem-perature Tc, the core temperature is a function ofthe power loss, and the power loss is a function ofRo. We use an iterative loop in a Java applet tomodel the core temperature and the life since theESR varies with temperature and ripple current. This leads to the question, What do we mean bythe “end of life,” anyway? How many capacitorsare allowed to fail, and what constitutes a failure?For example, one manufacturer might make a na-ive and untenable statement such as “None of ourcapacitors will fail before their rated life expires.”Other capacitor manufacturers might state that nomore than 10% of their capacitors will have failedby the end of their rated life. Still others might adda confidence interval on a similar claim. It is important that the method of performing thelife test and of specifying the allowable degrada-tion be comparable among capacitor manufactur-ers. We use EIA standard IS-749 which specifiescapacitor mounting, maximum airflow, inter-ca-pacitor spacing, end-of-life definitions. It alsospecifies the lifetime as that time at which 10% ofthe capacitors have failed due to parametric fail-

ure (ESR more than twice the initial limit), and nomore than 10% due to open or short circuit. The CDE model for wearout lifetime assumesthat the lifetime is limited by wearout mechanisms(parametric drift), not by random failures whichmight suddenly occur during the life of the capaci-tor. Wearout tends to occur on a group of capaci-tors as an ensemble process, not uniformly distrib-uted over the capacitor life. See Figure 1. The timeto wearout of a capacitor bank is fairly insensitiveto the number of capacitors in the bank. We have found that the wearout lifetime distri-bution typically has a bell shape, and we modelthis as a normal distribution with a mean of 1.2Land a standard deviation of 0.1L. We are strivingto be able to state that the mean is greater than1.2L with 90% confidence. Stated another way, ourgoal is to say with 90% confidence that no morethan 10% of the capacitors will have failed fromwearout before t=L. Due to the expected distribu-tion, this would be about the same as saying with90% confidence that no more than 1% will havefailed from wearout before t=0.9L.

Improvements in capacitor lifetime

If one looks at the history of lifetime ratings oflarge aluminum electrolytic capacitors, one wouldfind that these have progressed from 1,000 hoursat 65 ºC 40 years ago to up to 15,000 hours at 105ºC today. This is a factor of 240 in the life, whileproviding more capacitance and higher ripple cur-rent handling in the same package. Several factors

Figure 1: Probability density and cumulative distribution functions for wearout lifetime

Probability Density and Cumulative Distribution Functions for Wearout LifeA Possible Distribution for Rated Wearout Life L = 100kh

00.10.20.30.40.50.60.70.80.91

0 20000 40000 60000 80000 100000 120000 140000 160000 180000

Time (hours)

Cum

ulat

ion

Dist

ribu

tion

Func

tion

(CDF

)

0.00E+005.00E-061.00E-051.50E-052.00E-052.50E-053.00E-053.50E-054.00E-054.50E-055.00E-05

Pro

babi

lity

Dens

ity

Func

tion

(PD

F)

CDF(norm) PDF(norm)

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have contributed to this accomplishment. These in-clude improvements in purity and stability of allof the capacitor materials and components, espe-cially the electrolyte. Also improved seal technol-ogy must receive some credit. Hence the life model that has been presented isexpressed independently of and is unaffected bythe capacitance and the voltage rating, and is rela-tively insensitive to the number of capacitors in acapacitor bank.

Distinguishing lifetime from reliability

Capacitor lifetime is limited by electrochemicaldegradation that proceeds in a fairly predictablefashion, accelerated by temperature and voltagestress. Along the way, however, random failuresare bound to occur if the population is large enough.These are generally unrelated to wearout, and areinstead linked to some latent weakness, usually inthe paper, foil, or connections. These failures aremost often short-circuits, and they may occur sud-denly and without warning, although occasionallycapacitors may begin to draw excessive leakagecurrent and generate sufficient hydrogen gas pres-sure to rupture the safety vent then subsequentlydry out and fail open circuit. During the manufacture of the capacitor, ratedvoltage and temperature are applied in the agingprocess. Capacitance, leakage current, and ESR aretested on a 100% basis. Usually we employ addi-tional screening techniques to attempt to weed outinfant mortalities. Such methods include burn-in,surge voltage test, and hot DC leakage test. At CDEat the present time, these screening methods mayweed out an additional 0.1-0.5% of weak capaci-tors which may fail early in the field. The yield oflarge high-voltage capacitors has increased from92% in 1990 to over 98% today. If the burn-in orother high--stress-screening processes are repeated,a small percentage (0.02-0.2%) may be expectedto fail each time.

Bank considerations

In the field, it is often the case that several ormany capacitors are connected in series and in par-

allel. Due to adverse effects of fuses (resistance,cost, size, inductance), it is usually only practicalto do this in a manner that unfortunately createsthe situation that when one capacitor fails short-circuit, the bank and system cease to function. It isthe case, therefore, that the failure rate of the bankis approximately equal to the number of capaci-tors in the bank multiplied by the failure rate ofeach capacitor. It is generally true that smaller capacitors (CVrating) are more reliable than larger capacitors. Butwhen a large CV is needed, the highest reliabilityis usually achieved by using a smaller number ofphysically larger capacitors. This is true for tworeasons. First, the lower number of terminals,welds, connections, potential failure sites of thefewer, large capacitors is an inherent reliabilityadvantage. Second, large capacitors are generallydesigned, constructed, and screened differentlyfrom small capacitors to withstand the applicationof a large amount of energy connected withminiscule impedance, which is the situation of acapacitor bank. That said, the capacitor design en-gineer can tailor the design of a large or small ca-pacitor to the application of his capacitor in a largecapacitor bank. But the larger capacitor has an in-herent advantage in this regard. Wearout lifetime ratings for large and small ca-pacitors are about the same. So, in summary, a priceis paid for high-energy banks with regards to reli-ability, but the wearout lifetime is essentially en-ergy-inelastic.

Reliability modeling

Even when manufacturing processes and mate-rials and screening methods are state-of-the-art,random failures will still occur in the field. Classi-cal methods to predict reliability of wet aluminumelectrolytic capacitors are MIL-HDBK-217 andBellcore. We are familiar with MIL-HDBK-217and use it often, but we consider the magnitudesof the FIT rates it predicts at moderate tempera-tures to be obsolete, as are life models of alumi-num electrolytic capacitors from the era when thehandbook was compiled and written. Interestingly,the factors of improvement in life and reliability

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are about the same. The MIL Handbook basically starts from themaximum rated conditions then states that the in-cidence of random failures diminishes by half foreach 20% drop in applied DC voltage and for each20 ºC drop in core temperature. What we have found is that the predicted failurerate at elevated temperature for small capacitors issomewhat high, usually by a factor of 2-10, but forlarge capacitors the MIL Handbook is too large bymore than a factor of 10. This is in part because ofincorrect scaling factors. For example, the failurerate of a capacitor is in actuality related strongly toits energy storage, which is proportional to thesquare of the rated voltage, and yet in the MILHandbook there is no reliability factor for the ratedvoltage, only for the capacitance. This capacitance-only factor (C0.18) is not correct because it ignoresthe effect of voltage rating. We have also found that reliability approximatelydoubles every 10 ºC, not every 20 ºC. We do notdisagree with the voltage derating factor, but wechoose to use a cube-law instead. What all this means is that for a typical 45-65 ºCapplication of large electrolytics, the MIL Hand-book may indicate a failure rate that is over 100times larger than for actual CDE capacitors. Webelieve the reasons are possibly due to excessiveconservatism in the military handbook’s tempera-ture and voltage factors, along with real improve-ments in the reliability of our aluminum electro-lytic capacitor performance over the past 30 years,associated with some of the same advances in life-time performance that we have already discussed.One might argue that production yield is related tofield reliability, and in that case we note particu-larly the yield improvements in large capacitors(greater than 300 joules) with voltage ratings of400VDC and higher.

Reliability data

We rely on customer field failure rate data be-cause from an economic and practical standpoint,it would be impossible to acquire sufficient up-to-date reliability information from our laboratory toassess our present levels of reliability performance

in the typical derated conditions that our custom-ers’ equipment experiences in the field. This is be-cause billions of unit-hours would be needed, re-quiring about a million units and a staff of 50people. Instead, we have had detailed discussionswith some of our major customers regarding theirapplications (bank quantity, temperature, ripplecurrent, applied voltage) and field-return history.In some cases, it was impossible to tell if some ofthe failures were caused by a capacitor failing, orwhether there was another cause, such as an IGBTshorting, causing the capacitor to be destroyed. Inthose cases, we assumed 50% liability for purposesof reliability estimation. This effort resulted in our acquiring tens of bil-lions of unit hours data in a variety of applicationsto give us a good baseline confidence in the 45-75ºC core temperature range where we most neededdata. Most of the field data experienced FIT ratesof 0.5-20 from 2”-3” diameter high-voltage capaci-tors in multiple-capacitor (2-24 caps) banks. We combined this wealth of field data with ob-servations from our lab regarding the effects of ca-pacitor size, design criteria (basically rated life andtemperature), core temperature, and voltage derat-ing. Our combined QA and Engineering labs con-tain about 60 ovens and 170 power supplies, ofwhich usually 80% or more are in use. We alsotook into account some published prior studies andthe small number of published reliability modelsfor aluminum electrolytic capacitors. We used allof these sources of information together to developan empirical best-estimate reliability model of ourpresent capacitor reliability.

Scalability issues

What we found with regard to performance ofvarious capacitor types and sizes was that: 1. Pre-mium grade capacitors are more reliable, 2. Equalenergy storage results in equal reliability. The second result above has further implications,viz.: 3. For a given capacitance, lower voltage rat-ings are more reliable, 4. For a given voltage, lowercapacitance is more reliable, 5. For a given CVrating, lower voltage is more reliable. Since ca-pacitor size (volume) is approximately proportional

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to CV1.5, we can also observe that: 6. For a givensize, lower voltage ratings are more reliable. As already mentioned, we have also observed that7. For a given bank stored energy, fewer capaci-tors give higher reliability, 8. The rate of random(pre-wearout) failures of a bank of capacitors isequal to the number of capacitors times the failurerate of a single capacitor. Lastly, as we have stated, we believe that: 9. Fail-ure rate doubles every 10 ºC hotter the capacitorcore is operated, and 10. Failure rate is proportionalto the cube of the ratio of the applied to rated volt-age.

CDE’s reliability model

We have developed a semi-empirical model forthe FIT rate λ for pre-wearout random failures thatsatisfies the 10 criteria outlined in the precedingsection.

λ = 400,000NVa3C0.52(Tc-Tm)/10 / LBVr2 (3)

This basically means that for a given capacitorfamily (type, such as CDE 550C), temperature, andvoltage derating, the failure rate is proportional tothe product of the rated voltage and the square rootof the capacitance. All of these variables have beencovered in the life equation except for the nominalcapacitance C (farads) and the number of capaci-

tors in the bank, N. The FIT rate λ can then beused as the parameter in the Exponential Distribu-tion, which we will discuss in the next section.

Reliability model for pre-wearout mortality

The manner in which the occurrence of failuresare distributed in time determines the appropriatefailure distribution. There are many standard dis-tributions, some of which are just special cases ofothers. The two distributions we will be using arethe Exponential Distribution with the λ parameterjust discussed for the random failures and the Nor-mal Distribution for wearout failures. The shape of a probability distributions dependson whether one is looking at the normalized in-stantaneous failure rate of the initial population,known as the Probability Density Function (PDF)f(t), the total area under which is normalized toequal unity; the proportion of units from the initialpopulation that have failed, which is the integralfrom time t=0 to the plotted time coordinate of thePDF, in other words the area under the PDF curve,known as the Cumulative Distribution Function(CDF) F(t); or the instantaneous failure rate of thesurviving population, known as the Hazard Func-tion (HF) h(t). For any distribution,

h(t) ≡ f(t)/[1-F(t)] (4)

FIT rate vs Applied Voltage and Core Temperature

1

10

100

1000

40 45 50 55 60 65 70 75 80 85 90

Tcore (ºC)

Failu

re R

ate

(FIT

(ppm

/khr

))

100%Vr 90%Vr 80%Vr 50%Vr

550C532T400DF2G

Figure 2: Failure rate model predictions for various applied voltages and core temperatures

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The nature of the Exponential Distribution is thatits hazard rate has a constant value of λ. This meansthat the initial failure rate is λ and even after unitsfail, the failure rate of the remaining units retainsthe same λ value. Thus we have for the pre-wearout failures a prob-ability density function

fexp(t) = λe-λt (5)

and a cumulative distribution function

Fexp(t) = 1 - e-λt (6)

leading to a hazard function

hexp(t) = λ = FIT Rate (ppm/kh) (7)

Examples of FIT rate and MTBF

The Mean Time Between Failures is the recipro-cal of the FIT rate,

MTBF = 1 / λ = 1/FIT (Gh) (8)

and it is straightforward to deduce its units andmeaning. See Table 2 for a summary of commonunits. The units of FIT are ppm/kh, which is fail-ures per billion unit hours, or nanofailures per unithour. When we reciprocate this unit, we obtain theunits of gigahours. The main way to keep the di-mensions straight is to use the units if they aregiven, and if they are given in FIT, remember thatthe FIT is expressed in ppm/kh so its reciprocal isbillions of unit hours.

As an example, suppose we have a capacitoroperating at λ=200 FIT in a bank of N=10 capaci-tors, operating 4,300 hours per year. (A) What is the MTBF of a single capacitor andof the bank? For the capacitor, from equation (8) itis MTBF = 1/(200FIT) = 1 Gh/200 = 5 millionhours. For the bank, we divide the MTBF of asingle capacitor by the number of capacitors in thebank to obtain 500 kh. (B) At what time do we expect to have had α=1%of the capacitors to have failed? This would beapproximately 0.01*MTBF = 50 kh. To calculatemore precisely we may set equation (6) toF(tα)=0.01 and solve for tα as follows:

tα = -ln(1-α)/λ = 50,252 h (9)

(C) What percentage of the banks will have failedat the time when 1% of the capacitors have failed?Since there are 10 capacitors per bank and 1% ofthe capacitors have failed, we might expect thereto be 10% bank failures. This is indeed approxi-mately true. The best way to calculate the cumula-tive proportion of bank failures β precisely is tosubtract from unity the probability of survival ofall N=10 capacitors when we expect proportion αof the capacitors to have failed. Thus we have acumulative bank failure value of

β = 1-(1-α)N = 1 - (1-.01)10 = 9.6% (10)

bank failures at t=50 kh. (D) We have 1,000 banks in the field operating4,300 hours per year. How many field returns dowe expect per year? The FIT rate of the capacitoris 200 and of the bank is 200N=2,000 FIT, so weexpect 2 of every thousand banks to fail every thou-sand hours. For 4,300 hours per year operating,that’s about 9 bank failures per year. Fortunately, most of CDE capacitors are exhib-iting far lower FIT rates than 200 in the field.

Calculating attrited lifetime

In practice, it is apparent that the lifetime of alarge group of capacitors may be shorter than pre-scribed by the wearout life rating L calculated fromTable 2: Summary of common dimensions of

failure rate (λ) and MTBF

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equation (1). This situation may occur when life isdefined in a manner to describe the time at whicha small percentage of large capacitor banks willhave failed. For example, if only 1% cumulativecapacitor bank failures can be tolerated, and thebanks contain 24 large high-voltage capacitors, itis quite possible that this will yield an “attrited life”of smaller duration than given by the wearout lifecalculation, as the example calculations of a bankof ten capacitors in the preceding section sug-gested. The level at which attrited life tα from equation(9) will be less than the wearout life L from equa-tion (1) depends on the maximum tolerable pro-portion of capacitor failures α and upon the ratioof L/MTBF. It turns out that by implementing afew approximations and performing some algebrawe have an approximate relationship that thecapacitor’s attrited life will be less than the wearoutlife L when the tolerable proportion of random pre-wearout failures α meets the following condition:

α < (11)

For example, when there are N=10 capacitors in abank, each rated 10 mF at 125 Vdc, and the ap-plied DC voltage is 100 Vdc, we will experience acapacitor bank life that is shorter than the predictedwearout life when we limit the proportion of ran-dom bank failures to 5%. Another way of lookingat this is to say that we predict the proportion of

banks that fail before reaching the predictedwearout life to be about 5%.

Optimally reliable capacitor bank

Notice that the failure rate model of equation (3)penalizes not only for high operating temperatures,but also for high stored energy and for a large num-ber of capacitors in the bank. It is apparent thatusing a small number of large capacitors is benefi-cial as are implementing voltage derating and main-taining a small heat rise ∆T. Continuing the above line of reasoning, perhapsthere is an optimum number of capacitors to main-tain a moderate temperature from ripple currentheating while storing only as much energy as isneeded. Adding more capacitors would be less re-liable due to the bank size and quantity of capaci-tors, and using fewer capacitors would result inenough self-heating from the ripple current as torender the bank less reliable. It turns out that, based on our reliability model,there is indeed an optimum number of capacitorsto achieve the lowest bank failure rate, and thiscan be derived as follows. Neglecting mutual heat-ing, ESR variation with temperature, heat transfercoefficient variation with temperature, variationsin thermal resistance with capacitor position withinthe bank, and the possibility that lowering the bankimpedance will change the total ripple current tothe bank, the core temperature rise ∆T of the ca-

Figure 3: Example of core temperature rise and failure rate versus number of capacitors

B a n k F IT a n d C o re T e m p e ra tu re Ris e v s Nu m b e r o f C a p s

0.1

1

10

100

1000

10000

100000

0 10 20 30 40 50

N (n u m b er o f cap s)

Hea

t Ris

e (ºC

) and

Fai

lure

Rat

e (F

IT)

^T FIT

NVr√C 2500

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pacitors in a bank with a fixed amount of ripplecurrent is inversely proportional to the square ofthe number of capacitors in the bank. Let us as-sume that there is a heat rise ∆T1 for a bank withonly one capacitor. In actuality this value may behigher than the melting point of aluminum, but itdoesn’t invalidate the argument. We have

∆T = ∆T1 / N2 (12)

and from equation (2)

λ = γ N 2 (13)

for constant γ . Setting

∂λ/∂N = 0 (14)

we obtain

N = (15)

so that

∆TOPT = 5 / ln2 = 7.2 ºC (16)

Thus we have the result that for the optimallyreliable capacitor bank for a fixed bank ripple andgiven capacitor design, the optimum number ofcapacitors is that number of capacitors which re-sults in a core temperature rise of 7.2 ºC. Figure 2shows the heat rise and FIT rate versus the numberof capacitors in the bank for a particular applica-tion. In actuality we find that very few customers de-sign their capacitor banks for such a small heat risedue to cost and size constraints. ∆T = 15 - 20 ºC isactually more typical. But most experienced com-ponent engineers would probably admit that inthese cases, adding capacitors would not only re-duce the operating temperature but also increasethe reliability.

Model for wearout life distribution

Obviously not all capacitors fail at precisely the

hour they reach the predicted wearout time L. Afew will fail before (generally less than 10%) andmany after. This brings up the question as to howthe wearout failures are distributed in time. For wearout we assume a Normal Distributionwith mean of µ=1.2L and standard deviation ofσ=0.1L. From the mean time µ and the standard devia-tion σ we compute a normalized coordinate

(17)

and from this we calculate the PDF as

fnor(t) = (18)

There is no closed-form formula for the CDF ofthe Normal Distribution, but most spreadsheets andengineering software have this built in. The cumu-lative distribution function is of course defined as

Fnor(t) = (19)

and a hazard function

hnor(t) = φnor(z)/[1- Φnor(z)] (20)

When one looks at Figure 1, one may wonderabout how the wearout distribution of a popula-tion of capacitors will affect the failure rate of largebanks of capacitors. After all, if we say that up to10% of the capacitors may have failed fromwearout by time t=L, then we may infer that 1%will have failed at some previous time, and hencethe proportion of failures of large capacitor bankswill have possibly exceeded 10% before the ratedwearout life of the capacitors. Fortunately the Nor-mal Distribution allows us to consider this prob-lem as follows. To predict the time distribution of wearout fail-ures of banks of N capacitors, we should shift theNormal Distribution curve’s mean value µ for asingle capacitor slightly to the left by an amountof time ∆µ sufficient to equate the value of the cu-mulative distribution function to be to equal to avalue of α/N instead of 0.10. We find

z ≡ t - µσ

φnor(z) / σ = e-z2/2

σ√2π

Φnor(z) = ∫-∞

zφnor(w) dw

∆T1 / N2

√∆T1 ln25

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∆µ = Fnor-1(0.1) - Fnor

-1(α/N) (21)

then adjust the value of µ as

µ‘ = µ - ∆µ (22)

Because the tails of the PDF function diminish sorapidly (as e-t^2), we generally find that this reducesthe predicted wearout life between 10-20% and nomore.

Melding pre-wearout and wearout distributions

We have discussed the two major componentsof the capacitor lifetime distribution, and we cal-culated the crossover point from wearout-limitedto attrition-limited lifetime of capacitor banks.Rather than needing to switch back and forth be-tween these two regimes, we asked ourselves ifthey could be combined into a single, hybrid dis-tribution with well-behaved properties of theirprobability density, cumulative distribution, andhazard functions. Cornell Dubilier has recently ac-complished this task, and the development is pre-sented here. The approach we took to develop a well-behavedhybrid CDF that we call the Expo-Normal Hybrid(ENH) Distribution was to define

Fenh(z) ≡ 1 - [1- Φnor(z’)] e-λt (23)

which leads to a well-defined PDF

fenh(z) = [λ (1- Φnor(z’)) + φnor(z’) ] e-λt (24)

where we make a distinction between z and z’ byrecalling that the mean of the normal distributionis adjusted slightly as discussed and presented inequation (22). We may also derive the hazard func-tion

henh(t) = λ + φnor(z)/[σ(1-Φnor(z))] (25)

Table 3 summarizes the distributions used andderived in this paper. Figure 4 on the next pageshows the successfully melded hybrid ENHdistribution.

Summary

We have presented the CDE wearout lifetimemodel and discussed the difference betweenwearout lifetime and “attrited lifetime,” defined aslifetime that is limited by reaching a certain por-tion of open-circuit or short-circuit failures. Wepresented a model for calculating the failure rateλ, also known as the FIT rate, and the MTBF 1/λ.We discussed the life and reliability of single ca-pacitors versus banks of capacitors. We reviewedthe circumstances under which a capacitor in anapplication would have a lifetime limited by reli-ability versus by wearout. Finally, we developedand presented a combined wearout - reliabilitymodel that we call the Expo-Normal Hybrid (ENH)reliability model. Hopefully these models will help serve as guide-lines for successful capacitor applications. Involv-ing CDE in the design and application develop-ment process will help ensure that a suitable levelof reliability is achieved.

Table 3: Summary of properties of statistical distributions related to random and wearout failures

φnor(z) = e-z2/2

√2πz ≡ t - µ

σ Φnor(z) = ∫-∞

zφnor(w) dw

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Cornell Dubilier Expo-Normal Hybrid (ENH) Capacitor Life DistributionCumulative Bank Failures vs (T,Va/Vr,N)

T=Core Temperature, Va/Vr=applied/rated DC voltage, N=number of capacitors in bank.

0

0.2

0.4

0.6

0.8

1

1.2

0 100000 200000 300000 400000 500000 600000 700000 800000 900000

time (hours)

Cum

ulat

ive

Ban

k Fa

ilure

s

(75ºC,1,1) (75ºC,1,10) (75ºC,0.8,1) (65ºC,0.8,10)

550C682T550GF2G

Figure 4: Examples of CDE hybrid life model distribution